Virtual motion

This is a very rough informal summary of work on Promise Theoretic agent models of motion. No differential equations were used (or harmed) during the performance of these studies. All models are built from causally independent cellular agents that have only NSEW nearest neighbour observability.

Detailed notes are here:

  1. Virtual Motion I: Motion of the 3rd Kind - Draft paper on virtual motion (2021)
  2. Virtual motion II: Notes on kinematics, dynamics, and relativity in Semantic Spacetime
  3. Virtual Motion III: Examples as cellular automata. TBD
Also, a related description of a model that reproduces the quantum behaviour of the Bell/Aspect experiment.
  1. Spacetime Entangled Networks (II) Bell characteristics and quantum similitude of active agent processes
  2. Entanglement of Software Agents: How some quantum weirdness may be explained by a software model
Software repository for simulations

I've created a number of simulations of information systems that possess a single internal state value that they can share with their neighbours. The rules for each agent are designed to generate wavelike behaviour with both quadratic and linear wave equation methods. Waves are quite complicated phenomena that are highly sensitive to information resolution. If we think of these as models of an elementary (e.g. quantum) spacetime then we find that conservation of energy and information are very difficult to achieve for recognizable phenomena like waves without maintaining much greater resolution in interior degrees of freedom than in exterior spacetime itself! In physics parlance, that means that the resolution of Hilbert space needs to be higher than for configuration space, which may seem counter intuitive!

A few rough screen shots of what virtual wave motion looks like on one and two dimensional square lattices. Every agent is a causally independent automaton that only shares its state with neighbours. Each agent "decides" what to do with the information from its neighbours independendently. There is no force, only passive influence by observation. The resolution of spacetime is quite low, with only (x,y) = 37x76 cells. In order to get recognisable stable behaviour, the interior resolution of states has to be much higher than this.

  1. A virtual string plucked in the middle sets up standing waves.

  2. A double slit model showing a configuration that could produce interference. The + and - signs show where state amplitude is positive or negative with approximate conservation.

  3. The starting phase of a visualization of the log(square amplitude) of waves gives a estimate of probability or energy affinity spreading from the double slits towards a "screen" on the right.

  4. Running the simulation above for longer, we see the waves spread and interfere.

  5. Running the simulation above for longer, we see the waves spread and interfere. When they reach the screen on the right, we can sum the energy arriving to give a plot of the detector pattern.

  6. Continuing the simulation above...

  7. Continuing the simulation above...

  8. Continuing the simulation above...

  9. Continuing the simulation above...notice how the energy distribution is still lumpy, with places of basically zero amplitude. This is affected by the finite size of the enclosure, leading to standing waves.

The mass diffusion simulation (four cases) considers how "particles", as we understand them in classical physics, could be represented as bodies with a separate "mass charge" idenfifier. A particle is a localized object that can carry momentum (as a separate process) and travels in a straight line. So we introduce mass elements or labels M. A virtual process psi is activated in a cell when the psi wave reaches a spacetime cell. Locations may have a "mass charge label" M that is only able to be propagated by neighbouring cells if they are activated by the psi wave, so the psi wave acts as fuel and as a guiderail for the separate motion semantics of the particle. The particle is dependent on the energy infusion from the psi wave. Maybe this virtual motion automaton is something like what's generated by the Bohm picture of QM. A process field expands like a wave breathing life into the vacuum. On waking, locations transmit mass charges in a predetermined direction. Shape changes with wave but hits detector locally.

In the "probable direction" models, we bring together all the previous explorations to formulate a model in which mass bodies surf on a psi wave that breathes life/energy into the spacetime agents. The virtual processes now carry a directional "clock" which informs the agents receiving them in which direction they "intend" to move. This applies the rotational eigenfunction concept used in the Finite State Machine models previously in a simplified way using the internal memory of the agents rather than the exterior state of the spacetime. State information can't be passed 100% reliably so there is non-determistic behaviour as agents get in each other's way. Mass coherence is lost due to this erroneous transfer, and particles tend to spread out over the wave front.